The Topology of Randomness

Alex Simpson (U edinburgh)

Wednesday 5th October, 2011 16:00-17:00 204


What properties would space have if it consisted only of random points? In this talk, I will look at the "topology" of such random space. The quotes are there because random space is not a topological space in the usual sense. However, a generalisation of point-set topology, defined using (universal) algebraic tools, does provide a canonical notion of random space. The approach also yields a novel perspective on the measure-theoretic "paradoxes" (e.g., the Banach-Tarski Theorem).

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